Secrecy logic: S -secrecy structures

Let S = 〈L, S〉 be a deductive system. An S -secrecy logic is a quadruple K = 〈FmL(V ),K,B, S〉 , where FmL(V ) is the algebra of L-formulas, K,B are S -theories, with B ⊆ K and S ⊆ K such that S ∩ B = ∅ . K corresponds to information deducible from a knowledge base, B to information deducible from the publicly accessible (or browsable) part of the knowledge base and S is a secret set, a set of sensitive or private information that the knowledge base aims at concealing from its users. To provide models for this context, the notion of an S -secrecy structure is introduced. It is a quadruple A = 〈A,KA, BA, SA〉 , consisting of an L-algebra A , two S -filters KA, BA on A , with BA ⊆ KA , and a subset SA ⊆ KA , such that SA ∩ BA = ∅ . Several model theoretic/universal algebraic and categorical properties of the class of S -secrecy structures, endowed with secrecy homomorphisms, are studied relating to various universal algebraic and categorical constructs.